A = azelaxes(az,el) returns
a 3-by-3 matrix containing the components of the basis at
each point on the unit sphere specified by azimuth, az,
and elevation, el. The columns of A contain
the components of basis vectors in the order of radial, azimuthal
and elevation directions.

The first column of A is the radial basis
vector [0.5000; 0.5000; 0.7071]. The second and
third columns are the azimuth and elevation basis vectors, respectively.

Azimuth angle specified as a scalar in the closed range [–180,180].
Angle units are in degrees. To define the azimuth angle of a point
on a sphere, construct a vector from the origin to the point. The
azimuth angle is the angle in the xy-plane from
the positive x-axis to the vector's orthogonal
projection into the xy-plane. As examples, zero
azimuth angle and zero elevation angle specify a point on the x-axis
while an azimuth angle of 90° and an elevation angle of zero
specify a point on the y-axis.

Elevation angle specified as a scalar in the closed range [–90,90].
Angle units are in degrees. To define the elevation of a point on
the sphere, construct a vector from the origin to the point. The elevation
angle is the angle from its orthogonal projection into the xy-plane
to the vector itself. As examples, zero elevation angle defines the
equator of the sphere and ±90° elevation define the north
and south poles, respectively.

Spherical basis vectors returned as a 3-by-3 matrix. The columns
contain the unit vectors in the radial, azimuthal, and elevation directions,
respectively. Symbolically we can write the matrix as

The spherical basis vectors at
the point (az,el) can be expressed in terms of
the Cartesian unit vectors by

This set of basis vectors
can be derived from the local Cartesian basis by two consecutive rotations:
first by rotating the Cartesian vectors around the y-axis
by the negative elevation angle, -el, followed
by a rotation around the z-axis by the azimuth
angle, az. Symbolically, we can write

The following figure
shows the relationship between the spherical basis and the local Cartesian
unit vectors.